The hosts had struggled to find a breakthrough before Rey slotted home from the spot with just two minutes to go.
Club America, Morelia and Leon started the day level on 16 points but the latter two sides could not match Club America's success.
Morelia did take a point, however, from a 2-2 draw at rock-bottom Atlante.
The home side twice led, through a Roberto Nanni penalty and a Alejandro Vela strike, but Morelia hit back on each occasion with goals from Hector Mancilla and Joel Huiqui.
Leon were beaten 1-0 at home by Chiapas, for whom Carlos Ochoa scored a first-half winner from the penalty spot.
Santos Laguna moved up to seventh after a 2-2 draw at Atlas.
Omar Bravo scored twice for the hosts with Javier Orozco and then Rafael Figueroa earning Santos a point.
Pachuca and Unam Pumas drew 0-0 while two goals from Fidel Martinez and a Pablo Aguilar effort gave Tijuana a 3-0 victory over Veracruz.
Guadalajara remain in the bottom three after squandering a 3-0 lead to draw at Tigres.
Goals from Aldo De Nigris, Marco Fabian and Carlos Fierro put the visitors in charge but Tigres came storming back to earn a point through Alan Pulido, a Juninho penalty, and a late Lucas Lobos effort.